

<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
  <meta charset="utf-8">
  
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  
  <title>3.4.1.4. TzSimple1 Material &mdash; OpenSees Documentation  documentation</title>
  

  
  
  
  

  
  <script type="text/javascript" src="../../../../_static/js/modernizr.min.js"></script>
  
    
      <script type="text/javascript" id="documentation_options" data-url_root="../../../../" src="../../../../_static/documentation_options.js"></script>
        <script type="text/javascript" src="../../../../_static/jquery.js"></script>
        <script type="text/javascript" src="../../../../_static/underscore.js"></script>
        <script type="text/javascript" src="../../../../_static/doctools.js"></script>
        <script type="text/javascript" src="../../../../_static/language_data.js"></script>
        <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
    
    <script type="text/javascript" src="../../../../_static/js/theme.js"></script>

    

  
  <link rel="stylesheet" href="../../../../_static/css/theme.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/css/custom.css" type="text/css" />
    <link rel="index" title="Index" href="../../../../genindex.html" />
    <link rel="search" title="Search" href="../../../../search.html" />
    <link rel="next" title="3.4.1.5. QzSimple1 Material" href="QzSimple1.html" />
    <link rel="prev" title="3.4.1.3. PySimple1 Material" href="PySimple1.html" /> 
</head>

<body class="wy-body-for-nav">

   
  <div class="wy-grid-for-nav">
    
    <nav data-toggle="wy-nav-shift" class="wy-nav-side">
      <div class="wy-side-scroll">
        <div class="wy-side-nav-search" >
          

          
            <a href="../../../../index.html">
          

          
            
            <img src="../../../../_static/OpenSeesLogo.png" class="logo" alt="Logo"/>
          
          </a>

          
            
            
          

          
<div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../../../search.html" method="get">
    <input type="text" name="q" placeholder="Search docs" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
</div>

          
        </div>

        <div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
          
            
            
              
            
            
              <p class="caption"><span class="caption-text">Applications for Users</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../../interpreters.html">1. OpenSees Interpreters</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../install.html">2. Installation</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="../../../userManual.html">3. Command Manual</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="../../modelCommands.html">3.1. Modelling Commands</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../analysisCommands.html">3.2. Analysis Commands</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../outputCommands.html">3.3. Output Commands</a></li>
<li class="toctree-l2 current"><a class="reference internal" href="../../materialCommands.html">3.4. Material Commands</a><ul class="current">
<li class="toctree-l3 current"><a class="reference internal" href="../uniaxialMaterial.html">3.4.1. uniaxialMaterial Command</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="Steel01.html">3.4.1.1. Steel01 Material</a></li>
<li class="toctree-l4"><a class="reference internal" href="Steel02.html">3.4.1.2. Steel02 Material</a></li>
<li class="toctree-l4"><a class="reference internal" href="PySimple1.html">3.4.1.3. PySimple1 Material</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">3.4.1.4. TzSimple1 Material</a></li>
<li class="toctree-l4"><a class="reference internal" href="QzSimple1.html">3.4.1.5. QzSimple1 Material</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../ndMaterial.html">3.4.2. nDMaterial Command</a></li>
<li class="toctree-l3"><a class="reference internal" href="../section.html">3.4.3. section Command</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../miscCommands.html">3.5. Misc. Commands</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../../userExamples.html">4. Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../messageBoard.html">5. Questions, Bugs &amp; Feauture Requests</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/license.html">6. Copyright and License</a></li>
</ul>
<p class="caption"><span class="caption-text">Framework for Developer</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/sourceCode.html">1. Source Code</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/build.html">2. Building Application</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/references.html">3. References</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/extend.html">4. Extending Application</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/contribute.html">5. Contributing Code</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../../developer/issues.html">6. Issues</a></li>
</ul>

            
          
        </div>
      </div>
    </nav>

    <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">

      
      <nav class="wy-nav-top" aria-label="top navigation">
        
          <i data-toggle="wy-nav-top" class="fa fa-bars"></i>
          <a href="../../../../index.html">OpenSees Documentation</a>
        
      </nav>


      <div class="wy-nav-content">
        
        <div class="rst-content">
        
          















<div role="navigation" aria-label="breadcrumbs navigation">

  <ul class="wy-breadcrumbs">
    
      <li><a href="../../../../index.html">Docs</a> &raquo;</li>
        
          <li><a href="../../../userManual.html"><span class="section-number">3. </span>Command Manual</a> &raquo;</li>
        
          <li><a href="../../materialCommands.html"><span class="section-number">3.4. </span>Material Commands</a> &raquo;</li>
        
          <li><a href="../uniaxialMaterial.html"><span class="section-number">3.4.1. </span>uniaxialMaterial Command</a> &raquo;</li>
        
      <li><span class="section-number">3.4.1.4. </span>TzSimple1 Material</li>
    
    
      <li class="wy-breadcrumbs-aside">
        
            
            <a href="../../../../_sources/user/manual/material/uniaxialMaterials/TzSimple1.rst.txt" rel="nofollow"> View page source</a>
          
        
      </li>
    
  </ul>

  
  <hr/>
</div>
          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
           <div itemprop="articleBody">
            
  <div class="section" id="tzsimple1-material">
<span id="tzsimple1"></span><h1><span class="section-number">3.4.1.4. </span>TzSimple1 Material<a class="headerlink" href="#tzsimple1-material" title="Permalink to this headline">¶</a></h1>
<p>This command is used to construct a TzSimple1 uniaxial material object:</p>
<dl class="function">
<dt>
<code class="sig-name descname">uniaxialMaterial TzSimple1 $matTag $tzType $tult $z50 &lt;$c&gt;</code></dt>
<dd></dd></dl>

<table class="colwidths-given docutils align-default">
<colgroup>
<col style="width: 17%" />
<col style="width: 17%" />
<col style="width: 67%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Argument</p></th>
<th class="head"><p>Type</p></th>
<th class="head"><p>Description</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>$matTag</p></td>
<td><p><em>integer</em></p></td>
<td><p>integer tag identifying material</p></td>
</tr>
<tr class="row-odd"><td><p>$soilType</p></td>
<td><p><em>integer</em></p></td>
<td><p>1 or 2. see note.</p></td>
</tr>
<tr class="row-even"><td><p>$tult</p></td>
<td><p><em>float</em></p></td>
<td><p>Ultimate capacity of the t-z material. see notes</p></td>
</tr>
<tr class="row-odd"><td><p>$Z50</p></td>
<td><p><em>float</em></p></td>
<td><p>Displacement at which 50% of tult is mobilized in monotonic loading.</p></td>
</tr>
<tr class="row-even"><td><p>$c</p></td>
<td><p><em>float</em></p></td>
<td><p>The viscous damping term (optional: default = 0.0). see note.</p></td>
</tr>
</tbody>
</table>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>soilType = 1 Backbone of t-z curve approximates Reese and O’Neill (1987)</p>
<p>soilType = 2 Backbone of t-z curve approximates Mosher (1984) relation.</p>
<p>The argument tult is the ultimate capacity of the t-z material. Note that “t” or “tult” are shear stresses [force per unit area of pile surface] in common design equations, but are both loads for this uniaxialMaterial [i.e., shear stress times the tributary area of the pile].</p>
<p>The viscous damping term (dashpot) on the far-field (elastic) component of the displacement rate (velocity). Nonzero c values are used to represent radiation damping effects</p>
</div>
<p>EQUATIONS and EXAMPLERESPONSES:</p>
<p>The equations describing PySimple1 behavior are described in <a class="reference internal" href="#boulangeretal1990" id="id1"><span>[BoulangerEtAl1990]</span></a>. Only minor changes have been made in its implementation for OpenSees.</p>
<p>The nonlinear t-z behavior is conceptualized as consisting of elastic (<span class="math notranslate nohighlight">\(t-z^e\)</span>) and plastic (<span class="math notranslate nohighlight">\(t-z^p\)</span>) components in series. Radiation damping is modeled by a dashpot on the “far-field” elastic component (<span class="math notranslate nohighlight">\(t-z^e\)</span>) of the displacement rate. Note that <span class="math notranslate nohighlight">\(z = z^e + z^p\)</span>, and that <span class="math notranslate nohighlight">\(t = t^e = t^p\)</span>.</p>
<p>The plastic component is described by:</p>
<div class="math notranslate nohighlight">
\[t^p = t_{ult} - (t_{ult} - t^p_0) \left [\frac{c z_{50}}{c z_{50} + | z_p - z^p_0|} \right ]\]</div>
<p>where <span class="math notranslate nohighlight">\(t_{ult} = \)</span> at the start of the current plastic loading cycle, <span class="math notranslate nohighlight">\(z^p_0 = z^P\)</span> at the start of the current plastic loading cycle, and c = a constant and n = an exponent that define the shape of the <span class="math notranslate nohighlight">\(t-z^p\)</span> curve.</p>
<p>The elastic component can be conveniently expressed as:</p>
<div class="math notranslate nohighlight">
\[t^e = C_e \frac{t_{ult}}{z_{50}} z^e\]</div>
<p>where <span class="math notranslate nohighlight">\(C_e\)</span> = a constant that defines the normalized elastic stiffness. The value of <span class="math notranslate nohighlight">\(C_e\)</span> is not an independent parameter, but rather depends on the constants c &amp; n (along with the fact that <span class="math notranslate nohighlight">\(t = 0.5 t_{ult}\)</span> at <span class="math notranslate nohighlight">\(z = z_{50}\)</span>).</p>
<p>The flexibility of the above equations can be used to approximate different t-z backbone relations. Reese and O’Neill’s (1987) recommended backbone for drilled shafts is closely approximated using c = 0.5, n = 1.5, and Ce = 0.708. Mosher’s (1984) recommended backbone for axially loaded piles in sand is closely approximated using c = 0.6, n = 0.85, and Ce = 2.05. TzSimple1 is currently implemented to allow use of these two default sets of values. Values of tult and z50 must then be specified to define the t-z material behavior.</p>
<p>Viscous damping on the far-field (elastic) component of the t-z material is included for approximating radiation damping. For implementation in OpenSees the viscous damper is placed across the entire material, but the viscous force is calculated as proportional to the component of velocity (displacement rate) that developed in the far-field elastic component of the material. In addition, the total force across the t-z material is restricted to tult in magnitude so that the viscous damper cannot cause the total force to exceed the near-field soil capacity. Users should also be familiar with numerical oscillations that can develop in viscous damper forces under transient loading with certain solution algorithms and damping ratios. In general, an HHT algorithm is preferred over a Newmark algorithm for reducing such oscillations in materials like TzSimple1.</p>
<p>Examples of the cyclic loading response of TzSimple1 are given in the following plots. Note that the response for tzType = 2 has greater nonlinearity at smaller displacements (and hence greater hysteretic damping) and that it approaches tult more gradually (such that t/tult is still well below</p>
<div class="align-center figure">
<img alt="../../../../_images/TzSimple1.gif" src="../../../../_images/TzSimple1.gif" />
</div>
<div class="admonition-example admonition">
<p class="admonition-title">Example</p>
<p>The following constructs a TzSimple material with tag <strong>102</strong>, soil type <strong>2</strong> (Mosher relationship for backbone), <span class="math notranslate nohighlight">\(t_{ult}\)</span> of <strong>0.734</strong> and a <span class="math notranslate nohighlight">\(Z_{50}\)</span> of <strong>0.0000254</strong>. C is set to <strong>0.0</strong> for zero damping.</p>
<ol class="arabic simple">
<li><p><strong>Tcl Code</strong></p></li>
</ol>
<div class="highlight-tcl notranslate"><div class="highlight"><pre><span></span><span class="nv">uniaxialMaterial</span> TzSimple1 <span class="mi">102</span>  <span class="mi">2</span>  <span class="mf">0.734</span>  <span class="mf">2.54</span>e-5  <span class="mf">0.0</span>
</pre></div>
</div>
<ol class="arabic simple" start="2">
<li><p><strong>Python Code</strong></p></li>
</ol>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">uniaxialMaterial</span><span class="p">(</span><span class="s1">&#39;TzSimple1&#39;</span><span class="p">,</span> <span class="mi">102</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mf">0.734</span><span class="p">,</span> <span class="mf">2.54e-5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>Code Developed by: <a class="reference external" href="https://faculty.engineering.ucdavis.edu/boulanger/">Ross Boulanger</a>, UC Davis</p>
<dl class="citation">
<dt class="label" id="boulangeretal1990"><span class="brackets"><a class="fn-backref" href="#id1">BoulangerEtAl1990</a></span></dt>
<dd><p>Boulanger, R.W., Curras, C.J., Kutter, B.L., Wilson, D.W., and Abghari, A. (1990). “Seismic Soil-pile-strcture interaction experiments and analysis”, Jornal of Geotechnical and Geoenvironmental Engineering, ASCS, 125(9):750-759.</p>
</dd>
</dl>
</div>


           </div>
           
          </div>
          <footer>
  

  <hr/>

  <div role="contentinfo">
    <p>
        &copy; Copyright 2020, The Regents of the University of California

    </p>
  </div>
  Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/rtfd/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. 

</footer>

        </div>
      </div>

    </section>

  </div>
  


  <script type="text/javascript">
      jQuery(function () {
          SphinxRtdTheme.Navigation.enable(true);
      });
  </script>

  
  
    
    <!-- Theme Analytics -->
    <script>
    (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
      (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
      m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
    })(window,document,'script','https://www.google-analytics.com/analytics.js','ga');

    ga('create', 'UA-2431545-1', 'auto');
    ga('send', 'pageview');
    </script>

    
    

  <style>
         .wy-nav-content { max-width: none; }
  </style>



</body>
</html>